Methods of scatter correction of x-ray projection data 2

ABSTRACT

A system and method for forming an adjusted estimate of scattered radiation in a radiographic projection of a target object, which incorporates scattered radiation from objects adjacent to the target object, such as a patient table. A piercing point equalization method is disclosed, and a refinement of analytical kernel methods which utilizes hybrid kernels is also disclosed.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is related to commonly owned U.S. patent applicationSer. No. 12/125,053, filed on May 21, 2008.

FIELD OF THE INVENTION

This invention relates to the correction of the effects of scatteredradiation on the x-ray radiographic projection of an object and inparticular as applied to Computerized Tomography (CT).

BACKGROUND

Referring to FIGS. 1 a and 1 b, computerized tomography (CT) involvesthe imaging of the internal structure of an object 102 by collectingseveral projection images (“radiographic projections”) in a single scanoperation (“scan”), and is widely used in the medical field to view theinternal structure of selected portions of the human body. Typically,several two-dimensional projections are made of the object at differentprojection angles, and a three-dimensional representation of the objectis constructed from the projections using various tomographicreconstruction methods. From the three-dimensional image, conventionalaxial, coronal, or sagittal CT slices through the object can begenerated. The two-dimensional projections are typically created bytransmitting radiation from a “point source” 105 through the object 102,which will absorb some of the radiation based on its size, density, andatomic composition, and collecting the non-absorbed radiation onto atwo-dimensional imaging device, or imager 110, which comprises an arrayof pixel detectors (simply called “pixels”). In the typical CT system,the radiation source 105 and imaging detector 110 are mounted on agantry 150 which rotates them around the object 102 being scanned. Sucha system is shown in FIG. 1 a. A line that goes through the pointradiation source 105, the center of rotation (known as the isocenter),and is perpendicular to the two-dimensional imager 110 is called theprojection axis 112. The point where the projection axis hits thedetector is known as the piercing point of the detector. Typically, thedetector piercing point is located at or near the center of the imagerin full-fan geometry (also known as centered-detector geometry).Described below is a variation called half-fan (offset-detector)geometry, wherein the detector array is offset, thus allowing for anincrease in the field-of-view (FOV) with a 360 degree scan rotation.

The source's radiation emanates toward the imaging device 105 in avolume of space defined by a right-circular, elliptical, or rectangularcone having its vertex at the point source and its base at the imagingdevice. For this reason, the radiation is often called cone-beam (CB)radiation. Most commonly, the beam is collimated near the source into arectangular cone or pyramid so that, when no object is present, the beamradiation only falls on the detector and not outside the detectorboundaries. Generally, when no object is present within the cone, thedistribution of radiation is substantially uniform on the imager.However, the distribution of the radiation may be slightly non-uniform.In any event, any non-uniformity in the distribution can be measured ina calibration step and accounted for. The projection axis may not be atthe center of the imager or the center of the object. It may passthrough them at arbitrary locations including very near the edge.

FIG. 1 b shows further aspects of the CT system of FIG. 1 a, includinggantry 150 and controller 155. Controller 155 is coupled to radiationsource 105, imaging device 110, and user interface 115. User interface115 provides a human interface to controller 155 that enables the userto at least initiate a scan of the object, and to collect measuredprojection data from the imaging device. User interface 115 may beconfigured to present graphic representations of the measured data.

In an ideal imaging system, rays of radiation travel along respectivestraight-line transmission paths from the source, through the object(where they are partially absorbed), and then to respective pixeldetectors without generating scattered rays that are detected. However,in real systems, when a quantum of radiation is absorbed by a portion ofthe object, one or more scattered rays are often generated that deviatefrom the transmission path of the incident radiation. These scatteredrays are often received by “surrounding” detector elements that are notlocated on the transmission path that the initial quantum of radiationwas transmitted on, thereby creating measurement errors.

The measurement errors created by scattered radiation cause artifactsand loss of spatial and contrast resolution in the radiographicprojection data and the CT images produced by the radiation imagingsystem. The scattered radiation can also cause numerical errors in theimage reconstruction algorithms (generally referred to as “CT numberproblems” in the art). All of the foregoing leads to image degradation.

Scattered radiation may arise from many sources. These may include: thebow-tie filter (if present), the object being scanned, an anti-scattergrid (if present), and the detector housing. One model for addressingthese aforementioned scattering sources is described in U.S. patentapplication Ser. No. 12/125,053, filed on May 21, 2008, corresponding topatent publication number 20090290682, published Nov. 26, 2009. Thisapplication is hereby incorporated by reference in its entirety.

As indicated by both experiment and by Monte Carlo simulations,different types of objects can have different scattering properties andif they are all in the imaging field-of-view at the same time, then theymust be appropriately addressed by a scatter correction method. Forexample, a significant amount of scatter can come from objects (e.g.,supporting structures) adjacent to the actual object(s) of interest(e.g., the human body). One type of supporting structure is the patienttable which is commonly made of polycarbon, a light material having ahigh probability of Compton interactions. It has been found that thescatter correction method described in the incorporated application maynot be optimized to effectively model scatter from sources such as thepatient table, due to how its shape, position, density, and materialcomposition differ from that of the human body. As a result, scatter isunderestimated for some projections, and a cupping artifact is observedin patients below the isocenter region when using the half-fan geometrywith an offset detector (described and shown in FIG. 2). A method andsystem for estimating and correcting for scatter from multiple types ofobjects including the patient table is described hereinafter.

SUMMARY OF THE INVENTION

Disclosed herein are systems, methods, computer-program products, andcomputer-readable media for forming an estimate of total scatteredradiation in a radiographic projection of a target object positionedadjacent to or on an adjacent structure or object such as a patienttable. One such method includes:

-   -   a) generating at least one radiographic projection of the target        object;    -   b) forming a first scatter correction estimate of the        radiographic projection, the first scatter correction estimate        not including scatter from an adjacent object that is at least        partially adjacent to the target object;    -   c) separately forming a second scatter correction estimate of        the radiographic projection, the second scatter correction        estimate including scatter from the adjacent object; and    -   d) generating the total estimate of scattered radiation by        summing the first scatter correction estimate and the second        scatter correction estimate.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 a is a schematic diagram of a radiation imaging system accordingto the prior art.

FIG. 1 b is a schematic diagram of an exemplary radiation imaging systemembodiment which could be used to implement some of the inventionsdisclosed herein. Included is a gantry and a controller.

FIG. 2 is a transaxial view showing an exemplary configuration of thepatient table with respect to the object on the table (generally thepatient), the radiation source, and the detector, for two different(opposing) radiation angles as provided by rotation of the gantry aboutthe object. The half-fan (or offset-detector) geometry is illustrated.Two projections, situated 180 degrees apart, are shown.

FIG. 3 shows an example of a CT projection with a cupping artifact 300caused by scatter from the patient table.

FIG. 4 is a diagram showing how the influence of patient table scatteris magnified for lateral views.

FIG. 5 a shows an exemplary graph of piercing point projection values asa function of projection angle, before correction with the piercingpoint equalization correction.

FIG. 5 b shows an exemplary graph of piercing point projection values asa function of projection angle, after correction with the piercing pointequalization correction.

FIG. 5 c shows a high level flow diagram of an exemplary piercing pointmethod.

FIG. 5 d shows examples of caching.

FIG. 6 shows a high level flow diagram of an exemplary hybrid kernelmethod.

FIG. 7 is a particular instance of a graph of primary error vsprojection angle near the piercing point, using the kernel algorithmwith w=0.

FIG. 8 shows a transaxial view of the source-detector system with thepatient table in the field-of-view.

FIG. 9 illustrates the generation of a distance-weighted table mask.

FIG. 10 illustrates the process of computing a distance from the tableto the detector plane.

FIG. 11 shows an example of masks from binary and variable segmentationalgorithms, for the same projection.

FIG. 12 shows an exemplary graph of estimated scatter and measuredscatter signal vs. detector column, without and with analytical hybridkernel method correction for patient table scatter.

FIG. 13 shows corrected pelvis CT slices corresponding to theuncorrected slice of FIG. 3.

DETAILED DESCRIPTION

The inventive methods will be described according to embodimentsaddressing scattering from a scattering object adjacent to the targetobject or object of interest. An example thereof is a patient tablewhich acts as a supporting structure for the object of interest. Theseembodiments are exemplary and not limiting. The methods and systemsdescribed herein can be applied to scattering from other objectsadjacent to the object of interest.

The methods and associated systems and computer program products may beused alone or in various combinations with one another. As used hereinand in the claims, the action of obtaining an item, such as an estimateof a quantity, encompasses the action of receiving the item from anoutside process, computer-program product, and/or system, and the actionof generating the item by the claimed process, computer-program product,or system.

The radiographic projections described herein are generated by atwo-dimensional imaging device irradiated by a radiation source spacedtherefrom to provide a space for the object of interest. The imagingdevice measures incident radiation at a plurality of pixels atcorresponding locations on a two-dimensional surface, and theradiographic projection comprises a two-dimensional surface and aplurality of radiation values corresponding to a plurality of pixellocations of the imaging device. Each radiation value or amount includesa primary radiation amount representative of the radiation reaching thecorresponding pixel along a direct path from the radiation source and ascattered radiation amount representative of other radiation reachingthe corresponding pixel.

Exemplary method embodiments broadly comprise obtaining an estimate of aradiation amount associated with a first location of the radiographicprojection, the radiation amount comprising at least one of a radiationamount emitted by the radiation source, a scattered radiation amount, orthe primary radiation amount at the first location. The exemplarymethods further comprise storing the estimate of the scattered radiationin a computer-readable medium.

Exemplary computer-program product embodiments broadly compriseinstruction sets embodied on a computer-readable medium which, whenexecuted by a processor of a computer system, cause the processor toimplement the actions of the exemplary method embodiment. Exemplarysystem embodiments broadly encompass a radiation source, atwo-dimensional imaging device, a processor, and a set of instructionsstored on a computer-readable medium to implement actions that includethe actions of the above exemplary method embodiment.

FIG. 2 shows an exemplary configuration of a patient table 200 withrespect to the object 205 on the table (generally the patient), theradiation source 210, and the detector 215, for two different radiationangles as provided by rotation of the gantry about the object along acircular trajectory 212. In this example, system coordinates are definedwith respect to the isocenter and the table angle. In FIG. 2, the xyplane is defined as the plane of the paper. The z axis extends out fromthe paper. The axes are shown in the insert: line 220 corresponds to thex-axis, line 222 corresponds to the z-axis. The angle is defined as 0degrees when piercing point ray 220 (defined herein as a ray from x-raysource 210 perpendicularly through the isocenter line 222, hitting thedetector 215 at piercing point 224) is directed perpendicularly to tablesurface 225, and is defined as 90 degrees or 270 degrees when incidentradiation beam is directed parallel to table surface 225. Herein thedirection of increasing angle will be defined as counter clockwise:i.e., 90 degrees is defined as being the leftmost source point. Detector215 is disposed substantially opposite radiation source 210. However, inthe half-fan geometry shown herein, the detector is offset from theprojection axis so that one edge 230 is substantially opposite radiationsource 210. The half-fan geometry illustrated herein is defined as beingoffset to the left. To completely define the system coordinates, thedirection of detector offset must be specified. Triangles 235 and 235′(“half-fans”) represent the fields-of-view of the projections at 90 and270 degrees respectively.

FIG. 3 shows an example of a CT pelvis slice with cupping artifact 300caused by scatter from the patient table. The patient table scatterartifact is most severe in situations with high scatter-to-primaryratios (SPR's) such as pelvis scans.

As shown in FIG. 4, the influence of patient table scatter is magnifiedfor lateral views, i.e., where the radiation angle as defined above isnear 90 degrees or 270 degrees. In that case, table top surface 400 isparallel or nearly parallel to x-ray beam 405, and table exit surface410 (which is a scattering medium) is situated relatively close todetector 415, thus yielding an unobstructed path for scattered radiationto hit the detector. For the half-fan detection geometry shown, thetable 420 is in the field-of-view only for projection 425 (270 degreesas defined), but not for projection 430 (90 degrees as defined).

Herein two exemplary methods are disclosed which may be applied toforming an estimate of total scattered radiation in a radiographicprojection of a target object positioned near an adjacent object, forexample the target object positioned on a patient table, which include aseparate correction for scattering from the adjacent object. Thesemethods can be used to estimate scattering from the sources adjacent tothe target object. The first exemplary method is an empirical methodthat exploits the data inconsistencies between opposing projections todetermine a correction factor, where the scattering is largest onopposing lateral projections (this may be known hereinafter as “PiercingPoint Equalization method”). The second exemplary method is ananalytically based method that uses a hybrid kernel model for the pointscatter profiles (this may be known hereinafter as “Hybrid KernelCorrection method”). Also disclosed are exemplary system embodimentsrelated to the above mentioned exemplary methods which broadlyencompass: a radiation source, a two-dimensional imaging device, aprocessor, and a set of instructions stored on a computer-readablemedium to implement actions that include the actions of the abovementioned exemplary methods.

Piercing Point Equalization

The Piercing Point Equalization method described hereinafter isapplicable to estimating scattering due to sources such as the patienttable. It is further applicable in general to providing a correction toother scatter estimation methods.

A piercing point on the detector of a CT system is defined as the pointwhere a primary ray, i.e. an unscattered ray, extending from theradiation source perpendicularly through the isocenter line (the axis ofrotation about which the mechanical gantry rotates, or the z-axis asdefined in FIG. 2) of the CT system intersects the detector. A piercingpoint ray, therefore, is a primary ray which extends from the sourceperpendicularly through the isocenter line to the detector.

The exemplary piercing point equalization method described hereinafteris based on the assumption that, in CT acquisitions, two piercing pointrays taken 180 degrees apart should produce identical measurements.However, due to scatter from adjacent objects such as patient tablescatter, two opposing piercing point measurements may not match. In thismethod as applied to patient table scatter, an initial scattercorrection is made which takes into account many scattering sources. Theassumption is made that, since other scattering sources have beenaddressed in the initial scatter correction, the difference between thehigher and lower of the two opposing piercing point measurements (i.e.,the amount of radiation received by the detector) may be due totable-induced scatter error. This error is calculated and a correctionis then applied to the entire set of projections affected by scatterfrom the general adjacent object, e.g., a patient table. The correctionis based on the difference between the two opposing, or nearly opposing,piercing point primary estimates after the initial scatter correction ismade (for example, according to the kernel methods disclosed inincorporated application Ser. No. 12/125,053. These will be hereinaftertermed the “standard kernel-based correction”.)

FIGS. 5 a and 5 b show exemplary graphs of piercing point projectionvalues as a function of projection angle, before (FIG. 5 a) and after(FIG. 5 b) correction with the piercing point equalization correctiondescribed below.

An embodiment of the piercing point equalization method is a delayedmode (or implementation). This is defined herein that extra processingis required after data acquisition finishes so that the viewing of thefinal images is delayed. This embodiment is illustrated hereinafter asapplied to patient table scatter. This embodiment is straightforward toimplement once a complete set of paired projections is available. Sincescatter from the adjacent object, e.g., the table, is expected to varyfrom projection to projection, temporal smoothing (i.e., smoothing fromone projection to the next) can be applied to the table scatter estimateto reduce noise-induced fluctuations. Assuming all projections areavailable, an exemplary algorithm of this method embodiment is describedbelow and illustrated in FIG. 5 c.

-   -   (500) Apply the standard kernel-based scatter correction to all        projections.    -   (505) Define a Region of Interest (ROI) centered at the piercing        point, e.g., 15×15 pixels. Measure the mean signal (p_(i)) for        each projection i within that ROI. This can be considered a        first smoothing.    -   (510) For each projection i, find its best matching opposite        projection j. Assuming p_(i)<p_(j), record two numbers for these        two projections: d_(i)=0 for projection i, and the positive        difference d_(j)=p_(j)−p_(i) for projection j. i and j are        reversible: in other words, p_(j) is defined as the larger of        the piercing point measurements for the two projections i and j.        The set of d_(i) and d_(j) forms a difference curve d, which        spans the entire 360°. Half the values in the difference curve,        i.e. the lower of each opposite projection pair, are zero.    -   (515) Smooth the difference curve d generated in step c), e.g.,        for each projection i, take a running average of the difference        over 11 projections around i. This can be considered a second        smoothing.    -   (520) For the higher valued projection of each projection pair,        subtract the smoothed difference value obtained in step d) at        that point from the entire projection.

Another embodiment of the piercing point equalization method is areal-time/quasi-real-time implementation (or mode). Real-time is definedherein that the reconstruction process can keep up with the dataacquisition rate so that, as soon as the acquisition is finished, i.e.,the gantry rotation completes, the final images are available. Thisembodiment is illustrated hereinafter as applied to patient tablescatter, but can be applied to scatter from general adjacent objects. Asis the case with the earlier described delayed implementation, thepiercing point correction is applied after an initial scatter correctionis made, which takes into account scattering from all sources but maynot be optimized for sources such as the patient table.

To apply the piercing point correction in real time, the data is takenin such a way that the first 180 degrees of projections do not contain,or only contain minimal amounts of, table scatter. The correction doesnot need to be actually applied before the paired projections becomeavailable. This requires, in the best case, that the gantry starts at acertain angle and rotates in a certain direction, depending on the waythe detector is offset which will be described in more detail below. Inclinical settings, this requirement may not be met, which necessitatesdelaying until paired projections are available. Thereal-time/quasi-real-time embodiment provides a method for implementingthe necessary delaying.

A practical way to delay the carrying out of the piercing pointcorrection while data are being acquired and reconstructed is to cacheprojections. A projection is called “higher scatter” if it containssubstantial adjacent object (e.g., table) scatter. In certain cases,depending on how the detector is offset, the rotation direction andstart angle of rotation, no opposing lower scatter projection is yetavailable to match the piercing point intensity. In these cases, it isnecessary to wait until the opposing projection becomes available at alater point in time. During the intervening time, the unpaired “higherscatter” projections are cached either in RAM memory, or on disk.Determination of the regions of expected higher and lower scatterprojections, and the resulting requirements for caching, depends onseveral criteria. An exemplary, though not necessarily complete, set ofthe criteria used to determine caching, as illustrated with tablescatter is:

-   -   1. Rays which go through the table but do not pass through the        object evidence the relatively highest amount of table scatter.        If such rays pass longitudinally through the table, i.e., have        the longest relative traversal through the table, the table        scatter is maximized. The highest scatter angle, according to        this criterion, is 270 degrees as defined in FIG. 2, i.e.,        parallel to the table surface with the source to the right. This        angle is the highest scatter for a half-fan geometry with the        detector offset to the left, since, as shown in FIG. 4, the        majority of rays pass longitudinally through the table and exit        the table near to the detector. The lowest scatter angle is        correspondingly 90 degrees, since as shown in FIG. 4, for the        half fan geometry with detector offset to the left, the rays do        not pass through the table at all for 90 degrees. In an        embodiment, the 180 degrees of the circle with the lowest        scatter angle in its center is defined as the lower scatter        semicircle, whereas the 180 degrees of the circle with the        highest scatter angle at its center is defined as the higher        scatter semicircle. In the geometry of FIG. 4, the lower scatter        semicircle is 0-180 degrees, the higher scatter semicircle is        180-360 degrees. This is further illustrated in FIG. 5 d.    -   2. If rays which go through the table emerge close to the        detector, the table scatter component is further increased.    -   3. If rays go through a long path through the object before        reaching the table, there won't be as many scattered rays        reaching the table, therefore the table scatter will be somewhat        lowered. However, this scatter lowering effect is not as large        as the scatter increasing effect of a ray emerging from the        table near the detector.

The amount of caching required depends, not only on the criteria listedabove, but also on the initial position of the source and detector, thedirection of rotation of the gantry, and the direction of offset of thedetector. Some examples are illustrated in FIG. 5 d.

-   -   1. For a gantry rotation 550 starting with the source at 270        degrees, the amount of projections required to be cached is        about ¼ of the total projections, or 90 degrees worth of        projections, whether the rotation is CW or CCW, since the first        90 degrees of projections are considered “high scatter”, and        there is no opposing projection available. The regions marked        “cached” in the figure apply for initial source position of 270        degrees, with CW rotation.    -   2. For a gantry rotation 560 starting with the source at zero        degrees, i.e., at the top, the amount of caching depends on the        direction of rotation. For CCW rotation, no caching is        necessary, since the first 180 degrees of projections are        considered “low scatter”, and when the “high scatter”        projections are reached, opposing projections are available. On        the other extreme, if the source starts at zero degrees and the        rotation is CW, a full 180 of projections are “high scatter”        without opposing projections available, and would ideally be        cached. A similar situation exists for 180 degree initial        position 565, although the directions are reversed.

Caching the projections may delay the time that the final image isreconstructed.

The time delay can be reduced by reducing the amount of projections thatare cached. It is found in experimental studies that satisfactoryresults can still be achieved by caching less than the optimal range ofprojections, e.g., less than 90 degrees of projections for initialposition of 90 or 270 degrees. 45 degrees of caching for 90 or 270degree initial position has been found to give acceptable results insome cases.

Note that it is possible to cache an arbitrary number of projections,not just 45 or 90 degrees. Note also that the piercing pointequalization, whether delayed or real-time, should be applied afterkernel scatter correction but before the logarithm operation (describedin incorporated application Ser. No. 12/125,053). Although mainlydirected to table or other adjacent object scatter, the piercing pointequalization method also tends to correct, or can be influenced by, anyother inconsistencies such as detector gain and lag effects.

The piercing point equalization algorithm is easily implemented and issubstantially blind to the particulars of the adjacent object scatteringproperties. Only a constant-value scatter estimate is determined foreach projection. Another scattering model is an analytical model such asthat described hereinafter.

Analytical Hybrid Kernel Model

The method described hereinafter is related to the kernel modeldescribed in incorporated patent application Ser. No. 12/125,053.Application Ser. No. 12/125,053 introduced asymmetric kernels tocharacterize scatter profiles. Asymmetric kernel modeling of thescattering profiles extended the results for estimated object scatter ascompared to earlier symmetric kernel models. The symmetric andasymmetric kernel models are described in application Ser. No.12/125,053. The symmetric kernel model is termed Convolution Mode 0, andthe asymmetric kernel model is termed Convolution Mode 1. The currentmethod modifies the existing kernels where there is a shadow from ascattering source adjacent to the object, e.g., table shadow, in eachprojection, to reflect the additional scatter generated by thescattering source. These modified kernels are a blend of symmetrickernels and asymmetric kernels, and are termed “hybrid kernels”. Thismethod is illustrated hereinafter by an embodiment as applied to patienttable scatter. The application to patient table scatter is not limiting:the method may be applicable to other scattering sources adjacent to theobject.

For the exemplary patient table scatter embodiment, it has been foundexperimentally and by modeling such as Monte Carlo simulations thatx-ray beams which pass mainly through the patient table and not throughthe target object are better modeled by a symmetric kernel, whereasbeams that pass through the object are better modeled by an asymmetrickernel. This is possibly due to the differences in density, shape, andmaterial composition between the table and the target object. For thebeams passing through the patient table and the target object, acombination of symmetric and asymmetric kernels can be used. Referringback to FIG. 2, 0 degree beams have a larger asymmetric kernelcontribution since most scatter is from the object, whereas 90 degreebeams, i.e., lateral views, have a larger symmetric kernel contribution,since a higher proportion of scatter is from the table.

Accordingly, an embodiment of an algorithm is proposed that contains aspatially dependent mix of both symmetric and asymmetric kernels, withthe mixing fraction depending on the table structure and the projectionangle as follows:

HybridKernel=w·Kernel_(A)+(1−w)·Kernel_(B)

where Kernel_(A) is the symmetric kernel, Kernel_(B) is the asymmetrickernel, and w is a weighting factor, in an embodiment w being a functionthat depends on the geometry of the adjacent object, e.g., the table,and the gantry angle, and is calibrated with the aid of a slit scan aswill be described.

As described in incorporated application Ser. No. 12/125,053, theincident radiation I_(I) can be modeled as an array of pencil beams. Inan embodiment of the hybrid kernel model, the hybrid kernels are onlyapplied to pencil beams that pass through the adjacent object, e.g., thetable. Thus, the algorithm requires knowledge of the projected adjacentobject, e.g., table, shape and its position for each view. With thisknowledge, the hybrid kernel modification can be implementedsubstantially within the existing algorithm framework.

FIG. 6 shows a high level flow diagram of an exemplary hybrid kernelmethod embodiment as applied to a patient table adjacent object.

For each projection,

-   -   1) Generate a weighting factor (w(θ)) where θ is the projection        angle. (600)    -   2) Project the table onto the detector. Divide the detector area        into two regions—the region that is shadowed by the table (R1)        and the region that is not shadowed by the table (R2). (605)        Segmentation and/or variable mask may be utilized.    -   3) Within the convolution loop:        -   a. For region R2, proceed with regular asymmetric kernels            (conv1). (610)        -   b. For region R1, calculate scatter using both symmetric            (conv0) and asymmetric (conv1) kernels. The scatter            originating from R1 is given by: scatter=w*conv0+(1−w)*conv1            (615)        -   c. Sum up the scatter estimates from R1 and R2 regions to            produce the complete scatter estimate. (620)            Note that 3 a and 3 b can be rearranged during            implementation such that the conv1 is performed all together            for regions R1 and R2.            Following is a more detailed description of some of the            above method steps. Determination of weighting function w            (refer to step 600)

For each projection and each detector pixel shadowed by the table, theweighting function w defines how much of the total scatter signal iscoming from the table (in some embodiments, “super-pixels” comprisingmultiple pixels are utilized in order to lower computation time). Theweighting function specifies the fractional amplitude of the symmetrickernel relative to the total kernel amplitude. When the weight is 1, thekernel becomes completely symmetric; when it is 0, the kernel isasymmetric. The weighting function is projection-dependent and has apeak near the projection where the x-ray beam passes horizontallythrough the table (FIG. 2, 270° projection). In an embodiment, theweighting function is approximated as a symmetric Gaussian function

$\begin{matrix}{{{w(\theta)} = {A_{t}^{- \frac{{({\theta - \theta_{0}})}^{2}}{2\sigma^{2}}}}},} & (2)\end{matrix}$

where θ is the projection angle and A_(t), θ₀ and σ are parameters to bedetermined. The function is evaluated in the range [θ₀−180°, θ₀+180°] toensure its continuity upon the wraparound at 360°. The weightingfunction depends on the type of table used, but for a given table, ithas been found to be relatively independent of the scanned object shapeand size.

In an embodiment, a set of experimental measurements known as slit-scanscatter measurements may be used to obtain the weighting function, i.e.,to experimentally determine the weighting function for a particularpatient table. The general technique used in this embodiment is tocompare the existing kernel function correction with a slit-basedcorrection which is considered to be the “gold standard” correction.Slit-based correction is described in U.S. Pat. No. 7,336,760, issuedFeb. 26, 2008, which is hereby incorporated by reference in itsentirety. Then, from the difference curve between the two corrections,fitting parameters may be determined for the functional form chosen forthe weighting function. An exemplary weighting function determination isas follows:

A uniform elliptical phantom may be placed on the table and scanned withboth wide and narrow slit beams. The wide scan may be corrected with thecurrent kernel-based scatter correction algorithm. This is equivalent toa weighting function w=0 for all projections. The wide scan may also becorrected with the slit-based correction (scatterestimate=1.1*(wide−narrow)), which is considered to be the most accuratecorrection. From the slit-scan measurement, errors in the primary andscatter estimates using the standard kernel model may be determined and,from these results, a weighting function w may be generated. FIG. 7 is aparticular instance of a graph of primary error versus projection anglenear the piercing point, using the kernel algorithm with w=0. The erroris considered to be caused by table scatter.

It is observed that the fitting parameters for the weighting functionw(θ) are correlated with like parameters from the error curve of FIG. 7.For the Gaussian weighting function form of equation (2), two of thefitting parameters, θ₀ (this parameter depends on where the 0°projection is, ranges from 0 to 360) and σ, (this parameter ranges from15 to 40 degrees, with a typical value of 25 degrees) may be measureddirectly or indirectly from the peak location 705 and the FWHM 710 ofthe peak of the error curve. The third parameter in the weightingfunction, A_(t) (which ranges between 0 and 1) may then be manuallyadjusted to minimize primary errors. In an example, the following valueswere found, θ₀=210°, σ=25.5°, A_(t)=0.8.

Depending on the patient table geometry, a Gaussian form for theweighting function may not be optimal. Another possible form for theweighting function is a Gamma distribution.

Segmentation (refer to step 605)

In an embodiment of the hybrid kernel model as applied to table scatter,the hybrid kernels are applied to the pencil beams located only withinparts of the projection that are shadowed by the adjacent object, e.g.,the table. Thus it is important to be able to efficiently segment theadjacent object. The segmentation process will be illustrated with apatient table, although this is exemplary and not limiting.

Although it may be possible to use image processing techniques todetermine where the table shadow falls on the detector, it has beenfound to be more straightforward and more accurate to use a prioriknowledge of the table shape and position to mathematically project thetable onto the detector surface. An exemplary implementation of such aprojection is as follows:

The four edges of the table are projected on the detector. For scans inwhich the table is uniform in its axial direction, this turns intoprojecting four parallel lines, or effectively four points due to thetranslational symmetry in the axial direction. FIG. 8 shows a transaxialview of the source-detector system with the patient table 800 in thefield-of-view. Assuming the distance from the top 805 of the table tothe isocenter 810 is h, and the angle 815 between the table 800 and thecentral ray 820 is θ, then the four corner points 821-824 of the table'scross section can be fully specified in the coordinate system defined asin FIG. 8. At θ=0, the four points are:

$\begin{matrix}\left\{ \begin{matrix}{{p_{1}:\left( {x_{1},y_{2}} \right)} = \left( {h,{d/2}} \right)} \\{{p_{2}:\left( {x_{2},y_{2}} \right)} = \left( {{h + t},{d/2}} \right)} \\{{p_{3}:\left( {x_{2},y_{1}} \right)} = \left( {{h + t},{{- d}/2}} \right)} \\{{{p_{4}:\left( {x_{1},y_{1}} \right)} = \left( {h,{{- d}/2}} \right)},}\end{matrix} \right. & (3)\end{matrix}$

where t is the table thickness 830, and d is the table's lateral width835. At an arbitrary projection angle θ, the new coordinates of thesefour points are calculated by a rotational operation:

$\begin{matrix}\left\{ \begin{matrix}{x^{\prime} = {{x\; {\cos (\theta)}} - {y\; {\sin (\theta)}}}} \\{y^{\prime} = {{x\; {\sin (\theta)}} + {y\; {{\cos (\theta)}.}}}}\end{matrix} \right. & (4)\end{matrix}$

Applying Eq. (4), the new coordinates are:

$\begin{matrix}\left\{ \begin{matrix}{p_{1}^{\prime}:\left( {{{h\; \cos \; (\theta)} - {{d/2}\; {\sin (\theta)}}},{{h\; \sin \; (\theta)} + {{d/2}\; {\cos (\theta)}}}} \right)} \\{p_{2}^{\prime}:\left( {{{\left( {h + t} \right)\; \cos \; (\theta)} - {{d/2}\; {\sin (\theta)}}},{{\left( {h + t} \right)\; \sin \; (\theta)} + {{d/2}\; {\cos (\theta)}}}} \right)} \\{p_{3}^{\prime}:\left( {{{\left( {h + t} \right)\; \cos \; (\theta)} + {{d/2}\; {\sin (\theta)}}},{{\left( {h + t} \right)\; \sin \; (\theta)} - {{d/2}\; {\cos (\theta)}}}} \right)} \\{p_{4}^{\prime}:{\left( {{{h\; \cos \; (\theta)} + {{d/2}\; {\sin (\theta)}}},{{h\; \sin \; (\theta)} - {{d/2}\; {\cos (\theta)}}}} \right).}}\end{matrix} \right. & (5)\end{matrix}$

New points p′₁, p′₂, p′₃ and p′₄ can then be projected onto the detectorplane (defined to be in the x-plane) according to the followingequation:

$\begin{matrix}{{x_{p} = {x \cdot \frac{SDD}{{SAD} + y}}},} & (6)\end{matrix}$

where SDD is the Source-to-Detector Distance and SAD is theSource-to-Isocenter (Axis) Distance. The units of Eq. (6) can beexpressed in terms of the detector pixel index (or detector columnindex) as

$\begin{matrix}{{X_{p} = \frac{\left( {x_{p} - x_{0}} \right)}{pixelsize}},} & (7)\end{matrix}$

where x₀ is the x coordinate of the first detector column. Note that thepixel index Xp may or may not be located within the actual detectormatrix, so an intersection operation may be required.

After the four points are rotated and projected to the detector 840, thetable shadow on the detector plane is defined. It is the area betweentwo vertical lines passing through the leftmost and the rightmostpoints, with its width equal to the maximum separation among these fourprojected points. The part of the shadow that is actually seen by thedetector is the intersection of the projected shadow and the detectorarea, that is, the starting and the ending column of the table shade aregiven by:

$\begin{matrix}\left\{ \begin{matrix}{X_{1} = {\max \left( {{\min \left( {X_{p\; 1},X_{p\; 2},X_{p\; 3},X_{p\; 4}} \right)},1} \right)}} \\{{X_{2} = {\min \left( {{\max \left( {X_{p\; 1},X_{p\; 2},X_{p\; 3},X_{p\; 4}} \right)},{NSizeX}} \right)}},}\end{matrix} \right. & (8)\end{matrix}$

when the shadow does intersect with the detector. In thisimplementation, the table shadow or table mask is a binary 2-D maphaving values 1 and 0 for unshaded and shaded regions respectively.

Actual patient tables may not have exact rectangular cross sections. Onepossible alternate cross section is a trapezoidal cross section, whichmay be treated with the aforementioned scheme by adapting thecoordinates for the table edges in Eq. 3. Alternately, a slightlynon-rectangular cross section table may be approximated with arectangular cross section, with its height equal to the maximum tablethickness and width equal to the maximum table width.

For other table configurations, the thickness is not uniform axially.The table segmentation method is found to be robust even if the tablethickness is overestimated. This is because, in areas where the table isassumed to be thicker than it actually is, the scatter kernel value willbe 0 since the data measurements match the air measurements. Animportant datum is the knowledge of h, which is the distance from thetop of the table to the isocenter, thus defining the boundary of thetable top and the scanned object in the projection data.

Variable Mask (refer to step 605)

Further refinements to the segmentation method have been developed,which include allowing the adjacent object shadow, e.g., the tableshadow or mask, to be variable, rather than binary as in theabove-described exemplary segmentation implementation. This may improveestimation of the adjacent object scatter profile. The variable maskmethod is illustrated using a patient table, but this is exemplary andnot limiting.

The exemplary analytical table scatter correction algorithm as has beendisclosed has two main components—the weighting function and the tablemask. The weighting function is a scalar function and the table mask,corresponding to the detector area shaded by the table, is a binary 2-Dmap having values 1 and 0 for the regions R1 and R2, respectively. Thetwo combine to act as a pre-weighting step in the hybrid kernel model:

S(x,y)=(M _(edge)(x,y)·w·M _(table)(x,y)·A(I _(p)(x,y),I ₀(x,y)))

h _(sym)+(M _(edge)(x,y)·(1−w·M _(table)(x,y))·A(I _(p)(x,y),I ₀(x,y)))

h _(asym)′  (12)

where M_(edge) is the edge response mask, A is the amplitude part of thescatter kernel (a function of both the primary and the I₀ signal, asdescribed in incorporated patent application Ser. No. 12/125,053, w isthe weighting function and M_(table) is the table mask resulting fromtable segmentation.

In the refinement, instead of a binary map, the table mask may be madevariable. This means that each pencil beam passing through the table isallowed to have a different ratio of the symmetric to asymmetric kernelcomponent. The hypothesis behind this approach is that a pencil beamthat goes through the table closer to the detector may produce moresymmetric scatter than a pencil beam that intersects the table furtheraway from the detector, since it travels less distance in whichscattered rays from the table may be attenuated.

The actual dependence of the table map on the table-to-detector distanceis expected to be a complex function that would require extensiveresearch to determine. Herein discloses an exemplary estimate based onfirst principles. The assumption is first made that the table maskintensity value should be inversely proportional the table-to-detectordistance. The dependence is then adjusted based upon the scatter errorremaining after correction.

To generate the exemplary distance-dependent table mask, thetable-to-detector distance is computed for all pencil beams. For rayscutting through the table, the thickness of the table along the ray canbe significant compared to the table-to-detector distance. Thus, thetable-to-detector distance has ambiguities among the pencil beams.Because most table scatter comes from the table outer region, in thisapproximation the table-to-detector distance is calculated using theexit point for the table, although more complicated models could also beused.

Referring back to FIG. 8, after calculating the coordinates of the fourtable corners p′_(i) and their projected locations x_(pi) (i=1 . . . 4)on the detector, the table-to-detector distances are readily calculable.Note that in some cases, the projected corner may extend beyond theboundary of the physical detector. This corner would not be irradiatedand it is used only as a reference point. To include all referencepoints, a virtual detector may be created which is big enough to includeall corners of the table for all projections. The virtual detector usedin this exemplary implementation is 200 cm wide and centered so it spansa range from −1000 mm to +1000 mm, with pixel index running from 1 to2000 (pitch of 1 mm).

FIG. 9 illustrates an exemplary generation of a distance-weighted tablemask. Shown is the transaxial view of the table 900 with one of itssurfaces 905 projected onto the virtual detector 910. The distance fromtable surface 905 to detector 910 is approximated as a linearly varyingfunction having boundary values of d₂ and d₃ at endpoints x_(p2) andx_(p3). For a given projection, the two exit corners (p′₂ and p′₃)project to points x_(p2) and x_(p3) on the virtual detector withcorresponding distances of d₂ and d₃ to the table. Note that thedistances d₂ and d₃ are defined as the shortest geometrical distancefrom the table exit point to the detector. Then, for any ray fallingbetween p′₂ and p′₃, a distance estimate can be linearly interpolated.The linear interpolation method is only an approximation, since for adivergent beam the distance between two straight lines variesnonlinearly. Nevertheless, this approximation is expected to besufficiently accurate for a first estimate. The linearly interpolateddistance is computed as follows:

$\begin{matrix}{{{r_{ab}(x)} = {d_{a} + {\left( {d_{b} - d_{a}} \right)\; \frac{x - x_{pa}}{x_{pb} - x_{pa}}}}},} & (13)\end{matrix}$

where the subscripts a and b refer to two corner rays (in this case 2and 3).

FIG. 10 illustrates an exemplary process of computing a distance fromthe table to the detector plane. The distance to the detector using apair of table corners as a reference is first calculated, and allpermutations of table corners are used. (The final table-to-detectordistance is defined as the shortest distance to the detector.) Afterthis occurs, the virtual detector is clipped to the actual detector sizeand resampled to determine the final distance value for each superpixel.

Once a distance map r(x,y) is obtained, the table mask may be builtusing the formula

$\begin{matrix}{{{M_{table}\left( {x,y} \right)} = {k\left( \frac{DAD}{r\left( {x,y} \right)} \right)}^{q}},} & (14)\end{matrix}$

where DAD is the detector-to-axis distance, and k, q are user-determinedtuning parameters. It is found that k=1 and q=1 give reasonable results.

FIG. 11 shows an example of masks from binary (1100) and variable (1105)segmentation algorithms, for the same projection.

Results

FIG. 12 shows an exemplary graph of estimated scatter and measuredscatter signal vs. detector column, with (1200, 1205) and without (1210,1215) analytical hybrid kernel method correction for patient tablescatter. Upper curves 1220, 1225 are total signal, i.e.,primary+scatter. It is seen that, with the patient table correction, theestimated scatter curve is quite close to the measured curve.

FIG. 13 shows corrected pelvis CT slices corresponding to theuncorrected slice of FIG. 3. Slice 1300 is corrected using piercingpoint equalization, slice 1305 is corrected using the analytical hybridkernel model with a binary table mask. In this example, the analyticalcorrection gives an overall flatter image, measured as 40 HU (HounsfieldUnits) in the area below the isocenter.

System and Computer Program Product Embodiments

Each of the above-described methods may be implemented by computerprogram products that direct a computer system to perform the actions ofthe methods. Each such computer program product may comprise sets ofinstructions embodied on a tangible computer-readable medium that directthe processor of a computer system to perform the corresponding actions.Examples of such computer-readable mediums are the instruction memoryshown for controller 155 in FIG. 1 b. The instructions may be inexecutable computer code (such as C, C++), human-readable code (such asMatLab Code), and the like. Other types of tangible computer-readablemedia include floppy disks, removable hard disks, optical storage mediasuch as CD-ROMS, DVDs and bar codes, semiconductor memories such asflash memories, read-only-memories (ROMS), battery-backed volatilememories, networked storage devices, and the like. Given theabove-detailed description of the various method embodiments of theinventions of the present application, it is within the skill of one ofordinary skill in the tomography art to implement each of the methodembodiments disclosed herein in a computer program product without undueexperimentation. Such computer program product may be run on processor155 shown in FIG. 1 b, or on separate processors that are not coupled toCone-beam Computer Tomography Systems.

Exemplary systems of the present application may comprise radiationsource 105, imaging device 110, and controller 155, in combination withvarious computer program products and/or methods of the presentapplication.

Any recitation of “a”, “an”, and “the” is intended to mean one or moreunless specifically indicated to the contrary.

The terms and expressions which have been employed herein are used asterms of description and not of limitation, and there is no intention inthe use of such terms and expressions of excluding equivalents of thefeatures shown and described, it being recognized that variousmodifications are possible within the scope of the invention claimed.

Moreover, one or more features of one or more embodiments may becombined with one or more features of other embodiments withoutdeparting from the scope of the invention.

While the present invention has been particularly described with respectto the illustrated embodiments, it will be appreciated that variousalterations, modifications, adaptations, and equivalent arrangements maybe made based on the present disclosure, and are intended to be withinthe scope of the invention and the appended claims.

1. A method of forming a total estimate of scattered radiation in aradiographic projection of a target object, said scattered radiationdetected by a detector, said method comprising: a) generating at leastone radiographic projection of said target object; b) forming a firstscatter correction estimate of said radiographic projection, said firstscatter correction estimate not including scatter from an adjacentobject that is at least partially adjacent to said target object; c)separately forming a second scatter correction estimate of saidradiographic projection, said second scatter correction estimateincluding scatter from said adjacent object; and d) generating saidtotal estimate of scattered radiation by summing said first scattercorrection estimate and said second scatter correction estimate.
 2. Themethod of claim 1, wherein b) comprises dividing said at least oneradiographic projection into a first and a second portion, whereinexactly one of said first and said second portion, said second portion,includes a radiation projection of an adjacent object that is at leastpartially adjacent to said target object; and forming said first scattercorrection estimate of said first portion.
 3. The method of claim 1,wherein c) comprises separately forming said second scatter correctionestimate of said second portion.
 4. The method of claim 1, wherein saidadjacent object differs from said target object in at least one of:density, and material composition.
 5. The method of claim 1, whereinsaid adjacent object is a support structure for said target object. 6.The method of claim 5, wherein said adjacent object is a patient tabletop.
 7. The method of claim 6, wherein said patient table top comprisesa carbon fiber skin layer.
 8. The method of claim 1, wherein saidradiographic projection is formed from a radiation source onto adetector, said radiographic projection having a projection axis, saiddetector being offset from said projection axis.
 9. The method of claim2, wherein said second scatter correction estimate of said secondportion is formed using an analytical model.
 10. The method of claim 9,wherein said analytical model includes generating a scatter estimationkernel for said adjacent object.
 11. The method of claim 10, whereinsaid scatter estimation kernel for said adjacent object comprises ahybrid combination of at least a first scatter estimation kernel and atleast a second scatter estimation kernel.
 12. The method of claim 11,wherein said first scatter estimation kernel is a symmetric kernel andsaid second scatter estimation kernel is an asymmetric kernel, andwherein said hybrid combination includes a weighting factor wcorresponding to a relative weighting of said symmetric kernel and saidasymmetric kernel.
 13. The method of claim 12, wherein said weightingfactor w is a function of projection angle θ, i.e., a weighting functionw(θ).
 14. The method of claim 13, comprising for each projection: a)generating said w(θ); b) projecting said adjacent object onto saiddetector; c) dividing said detector into a first region R1 shadowed bysaid adjacent object, and a second region R2 not shadowed by saidadjacent object; d) forming a first scatter estimation using asymmetric(conv1) kernels for region R2; and e) forming a second scatterestimation using symmetric (conv0) and asymmetric (conv1) kernels forregion R1, of the form scatter=w*conv0+(1−w)*conv1; and f) forming atotal scatter estimation equal to the sum of said first scatterestimation and said second scatter estimation; and g) storing said totalscatter estimation on a computer-readable medium.
 15. The method ofclaim 14, wherein said regions R1 and R2 form an adjacent object mask,said adjacent object mask being a binary 2D map having values 1 and 0for regions R1 and R2 respectively.
 16. The method of claim 14, whereinsaid regions R1 and R2 form an adjacent object mask, said adjacentobject mask having a variable value between 0 and 1 for a given locationon said detector, said variable value having a dependence on thedistance between said given location on said detector and the exit pointfrom said adjacent object of a pencil radiation beam impinging on saidgiven location on said detector.
 17. The method of claim 16, whereinsaid dependence is inversely proportional.
 18. The method of claim 13,wherein said weighting function is approximated as a function containingweighting function parameters, said weighting function parameters beingderived from an experimental determination for a particular adjacentobject geometry.
 19. The method of claim 18, wherein said experimentaldetermination is provided by slit scan measurements.
 20. The method ofclaim 13, wherein said weighting function is approximated as one of: asymmetric Gaussian function, and an asymmetric Gamma distributionfunction.
 21. The method of claim 2, wherein said first scattercorrection estimate of said first portion is formed using an analyticalmodel including generating a scatter estimation kernel for said targetobject.
 22. The method of claim 21, wherein said scatter estimationkernel for said target object is an asymmetric kernel.
 23. Acomputer-readable medium configured to store instruction sets which,when executed by a processor of a computer system, cause the processorto estimate scattered radiation in a radiographic projection of a targetobject, the computer readable medium comprising: one or more instructionsets that directs the processor to perform the actions of a) generatingat least one radiographic projection of said target object; b) forming afirst scatter correction estimate of said radiographic projection, saidfirst scatter correction estimate not including scatter from an adjacentobject that is at least partially adjacent to said target object; c)separately forming a second scatter correction estimate of saidradiographic projection, said second scatter correction estimateincluding scatter from said adjacent object; and d) generating saidtotal estimate of scattered radiation by summing said first scattercorrection estimate and said second scatter correction estimate.
 24. Thecomputer-readable medium of claim 23, wherein b) comprises dividing saidat least one radiographic projection into a first and a second portion,wherein exactly one of said first and said second portion, said secondportion, includes a radiation projection of an adjacent object that isat least partially adjacent to said target object; and forming saidfirst scatter correction estimate of said first portion; and wherein c)comprises separately forming said second scatter correction estimate ofsaid second portion.
 25. The computer-readable medium of claim 23,wherein said adjacent object differs from said target object in at leastone of: density, and material composition.
 26. The computer-readablemedium of claim 23, wherein said adjacent object is a support structurefor said target object.
 27. The computer-readable medium of claim 26,wherein said adjacent object is a patient table top.
 28. Thecomputer-readable medium of claim 27, wherein said patient table topcomprises a carbon fiber skin layer.
 29. The computer-readable medium ofclaim 23, wherein said radiographic projection is formed from aradiation source onto a detector, said radiographic projection having aprojection axis, said detector being offset from said projection axis.30. The computer-readable medium of claim 24, wherein said secondscatter correction estimate of said second portion is formed using ananalytical model.
 31. The computer-readable medium of claim 30, whereinsaid analytical model includes generating a scatter estimation kernelfor said adjacent object.
 32. The computer-readable medium of claim 31,wherein said scatter estimation kernel for said adjacent object is ahybrid combination of symmetric and asymmetric kernels, said hybridcombination including a weighting factor w corresponding to relativeweighting of said symmetric kernels and said asymmetric kernels in saidhybrid combination.
 33. The computer-readable medium of claim 32,wherein said weighting factor w is a function of projection angle θ,i.e., a weighting function w(θ).
 34. The computer-readable medium ofclaim 33, comprising for each projection: a) generating said w(θ); b)projecting said adjacent object onto said detector; c) dividing saiddetector into a first region R1 shadowed by said adjacent object, and asecond region R2 not shadowed by said adjacent object; d) forming afirst scatter estimation using asymmetric (conv1) kernels for region R2;and e) forming a second scatter estimation using symmetric (conv0) andasymmetric (conv1) kernels for region R1, of the formscatter=w*conv0+(1−w)*conv1; and f) forming a total scatter estimationequal to the sum of said first scatter estimation and said secondscatter estimation; and g) storing said total scatter estimation on acomputer-readable medium
 35. The computer-readable medium of claim 34,wherein said regions R1 and R2 form an adjacent object mask, saidadjacent object mask being a binary 2D map having values 1 and 0 forregions R1 and R2 respectively.
 36. The computer-readable medium ofclaim 34, wherein said regions R1 and R2 form an adjacent object mask,said adjacent object mask having a variable value between 0 and 1 for agiven location on said detector, said variable value having a dependenceon the distance between said given location on said detector and theexit point from said adjacent object of a pencil radiation beamimpinging on said given location on said detector.
 37. Thecomputer-readable medium of claim 36, wherein said dependence isinversely proportional.
 38. The computer-readable medium of claim 33,wherein said weighting function is approximated as a function containingweighting function parameters, said weighting function parameters beingderived from an experimental determination for a particular adjacentobject geometry.
 39. The computer-readable medium of claim 38, whereinsaid experimental determination is provided by slit scan measurements.40. The computer-readable medium of claim 38, wherein said weightingfunction is approximated as one of: a symmetric Gaussian function, andan asymmetric Gamma distribution function.
 41. The computer-readablemedium of claim 24, wherein said first scatter correction estimate ofsaid first portion is formed using an analytical model includinggenerating a scatter estimation kernel for said target object.
 40. 42.The computer-readable medium of claim 39 41, wherein said scatterestimation kernel for said target object is an asymmetric kernel.
 43. Asystem comprising: a processor; and a computer-readable medium accordingto claim
 23. 44. A system comprising: a processor; and acomputer-readable medium according to claim
 24. 45. A system comprising:a processor; and a computer-readable medium according to claim
 32. 46. Asystem comprising: a processor; and a computer-readable medium accordingto claim 34.